Abstract

This paper considers the question of identifying the parameters governing the behavior of fundamental global network problems. Many papers on distributed network algorithms consider the task of optimizing the running time successful when an O(n) bound is achieved on an n-vertex network. We propose that a more sensitive parameter is the network's diameter $\Diam$. This is demonstrated in the paper by providing a distributed minimum-weight spanning tree algorithm whose time complexity is sublinear in n, but linear in $\Diam$ (specifically, $O(\Diam + n^\varepsilon \cdot \log^* n)$ for $\varepsilon = \frac{\ln 3}{\ln 6} = 0.6131...$). Our result is achieved through the application of graph decomposition and edge-elimination-by-pipelining techniques that may be of independent interest.

MSC codes

  1. 05C05
  2. 05C85
  3. 68Q22
  4. 68Q25
  5. 68R10

Keywords

  1. MST
  2. min-weight spanning trees
  3. distributed algorithms

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Published In

cover image SIAM Journal on Computing
SIAM Journal on Computing
Pages: 302 - 316
ISSN (online): 1095-7111

History

Published online: 28 July 2006

MSC codes

  1. 05C05
  2. 05C85
  3. 68Q22
  4. 68Q25
  5. 68R10

Keywords

  1. MST
  2. min-weight spanning trees
  3. distributed algorithms

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